# Juan José Mendoza Arenas

My research is devoted to the computational study of the properties of quantum materials. These systems consist of many interacting particles (e.g., electrons, impurities, phonons), are highly sensitive to external perturbations, and feature spectacular states of matter such as magnetic order and high-temperature superconductivity. This makes them very attractive for implementing and controlling diverse novel technologies. However, understanding their properties is extremely challenging, and many questions regarding their nature remain open.

To unravel the phenomenology of quantum materials, I rely on simple yet rich theoretical models (such as Heisenberg or Hubbard Hamiltonians) to capture their underlying physics, and on powerful tensor network algorithms to calculate their quantum states. In particular, my work focuses on ground-state phase diagrams of correlated systems, out-of-equilibrium (coherent and dissipative) control of superconductivity and magnetism, optimization of electric and energy transport, and quantum thermal machines. Furthermore, I am interested in the analysis of quantum materials through state-of-the-art quantum computers and simulators.

Currently I am also aiming at applying recently-developed tensor network approaches to solve partial differential equations, with particular applications to fluid turbulence and combustion.

M. Brenes, J. J. Mendoza-Arenas, A. Purkayastha, M. T. Mitchison, S. R. Clark and J. Goold, Tensor-Network Method to Simulate Strongly Interacting Quantum Thermal Machines, Phys. Rev. X 10, 031040 (2020).

J. J. Mendoza-Arenas, M. Znidaric, V. K. Varma, J. Goold, S. R. Clark and A. Scardicchio, Asymmetry in energy versus spin transport in certain interacting disordered systems, Phys. Rev. B 99, 094435 (2019).

J. J. Mendoza-Arenas, S. R. Clark, S. Felicetti, G. Romero, E. Solano, D. G. Angelakis and D. Jaksch, Beyond mean-field bistability in driven-dissipative lattices: Bunching-antibunching transition and quantum simulation, Phys. Rev. A 93, 023821 (2016).

J. J. Mendoza-Arenas, S. R. Clark and D. Jaksch, Coexistence of energy di usion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking, Phys. Rev. E 91, 042129 (2015).

J. J. Mendoza-Arenas, T. Grujic, D. Jaksch and S. R. Clark, Dephasing enhanced transport in nonequilibrium strongly-correlated quantum systems, Phys. Rev. B 87, 235130 (2013).

J. J. Mendoza-Arenas and S. R. Clark, Giant rectification in strongly-interacting boundary-driven tilted systems, arXiv:2209.11718 (2022).

J. J. Mendoza-Arenas, Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model, J. Stat. Mech. (2022) 043101.

J. J. Mendoza-Arenas and B. Buca, Self-induced entanglement resonance in a disordered Bose-Fermi mixture, arXiv:2106.06277 (2021).

R. Guerrero-Suarez, J. J. Mendoza-Arenas, R. Franco and J. Silva-Valencia, Spin-selective insulators in Bose-Fermi mixtures, Phys. Rev. A 103, 023304 (2021).

F. P. M. Méndez-Córdoba, J. J. Mendoza-Arenas, F. J. Gómez-Ruiz, F. J. Rodríguez, C. Tejedor and L. Quiroga, Rényi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems, Phys. Rev. Research 2, 043264 (2020).